MinT - Best Known (90−26, 90, s)-Nets in Base 5

Best Known (90−26, 90, s)-Nets in Base 5

(90−26, 90, 296)-Net over F₅ — Constructive and digital

Digital (64, 90, 296)-net over F₅, using

trace code for nets [i] based on digital (19, 45, 148)-net over F₂₅, using
- net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
    - a function field by GarcÃa and Quoos [i]

(90−26, 90, 848)-Net over F₅ — Digital

Digital (64, 90, 848)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(90−26, 90, 97797)-Net in Base 5 — Upper bound on s

There is no (64, 90, 97798)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 807 835956 009845 183354 103313 267451 150421 562266 159606 890068 622745 > 5⁹⁰ [i]